Answer the questions as much as you can

1What is the necessary condition for forward price to be equal futures price for underlying such as non-dividend stock or commodity? 3)What could/should be an alternative response of MGRM management to the loss on futures markets? 5 Discuss when price of European put is equal to value of European call, where underlying is non- dividend paying stock. When the value of European call is higher than value of European put? 6.Define and briefly discuss application of a commodity swap and a total return swap. Please cont rast (similarities and differences) both swaps with vanilla interest rate swap. 7.Discuss the importance of assumption of lack of default risk in application of principal method for interest rate swaps valuation. 8.Confirm that the forward price (for forward contract) is consistent with binominal tree valuation. 9 Explain why in the formula for risk neutral probability of up-move (in case of option on futures) do not contain exponent function (like in case of example discussed in class). 10 Define and discuss basic properties of following stochastics process: Brownian bridge, Cox - Ingersoll - Ross, Ornstein - Uhlenbeck 11 Assuming that st follow Geometric Brownian motion, please define and examine the properties of following stochastics process: a) 3 St b) Exp(St). 12) show that Black Scholes formula for European put option on non- dividend stock is a solution of Black -Scholes PDE